Differentiate the following function with respect to x: (2x^2-3) - Vidyadip

Question

Differentiate the following function with respect to x:

$(\text{2x}^2-3)\sin\text{x}$

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Answer

Let $\text{u}=\text{2x}^2-3;\text{v}=\sin\text{x}$

Then, $\text{u}'=\text{4x};\text{v}'=\cos\text{x}$

Using the product rule:

$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$

$\frac{\text{d}}{\text{dx}}[(\text{2x}^2-3)\sin\text{x}]=(\text{2x}^2-3)\cos\text{x}+\text{4x}\sin\text{x}$

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